Beizer circle messes up model
Looking at your 1st picture, your Curve is overlapping each other.

So your 3rd picture looks like having a double faces.

Better still, instead of using Bezier Curve + Curve Modifier, use your Bezier Curve to get the kind of Curve you are expecting from Curve Modifier and then Extrude.

After Extrude, you can do the thickness.